The Magic of Shamir’s Shares: BLS Threshold Signatures

Any t-from-n

I would say that the three greatest cybersecurity papers which have had the most impact are:

• Diffie, W., & Hellman, M. E. (2022). New directions in cryptography. In Democratizing cryptography: the work of Whitfield Diffie and Martin Hellman (pp. 365–390).
• Rivest, R. L., Shamir, A., & Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2), 120–126.
• Shamir, A. (1979). How to share a secret. Communications of the ACM, 22(11), 612–613.

For the New Directions paper, we still use the Diffie-Hellman method for our key exchange, and the RSA paper has led to nearly five decades of public key signing and encryption with RSA. To me, though, the third paper is just as good as the other two, and where Adi Shamir outlined how we can split a private key into a number of shares (n) and then define a threshold (t) to bring back the original key. This defines a (t,n) threshold system. And the great thing is that it is perfect security, and where you cannot rebuild the key with less than t shares.

So, let’s look at a practical example of Shamir’s threshold methods, and where we have a common message, and where we define the number of shares that can come…